A set of 47 disks are consecutively numbered 1 to 47 and placed in a row as follows: 1, 2, 3, 4, ... 45, 46, 47.
Rearrange the disks so for any two given disks A and B, the disk equal to their arithmetic mean doesn't lie between them. For example, Disk 4 cannot lie between Disk 1 and Disk 7 since the arithmetic mean of 1 and 7 is 4. However, since 7 is not equal to the arithmetic mean of 1 and 4, Disk 7 may lie between Disk 1 and Disk 4.
(In reply to
solution by Daniel)
But 5 is between 1 and 9; 8 is between 12 and 4. There are many others. Here's the set of 115:
43 23 3 18 26 34
1 5 9 39 35 31 18 30 42
1 9 17 39 31 23 22 26 30
1 13 25 39 27 15 22 30 38
1 17 33 39 23 7 22 34 46
1 21 41 35 31 27 26 30 34
5 9 13 35 27 19 26 34 42
5 13 21 35 23 11 30 34 38
5 17 29 35 19 3 30 38 46
5 21 37 31 27 23 34 38 42
5 25 45 31 23 15 38 42 46
9 13 17 31 19 7 44 40 36
9 17 25 27 23 19 44 36 28
9 21 33 27 19 11 44 32 20
9 25 41 27 15 3 44 28 12
13 17 21 23 19 15 44 24 4
13 21 29 23 15 7 40 36 32
13 25 37 19 15 11 40 32 24
13 29 45 19 11 3 40 28 16
17 21 25 15 11 7 40 24 8
17 25 33 11 7 3 36 32 28
17 29 41 2 6 10 36 28 20
21 25 29 2 10 18 36 24 12
21 29 37 2 14 26 36 20 4
21 33 45 2 18 34 32 28 24
25 29 33 2 22 42 32 24 16
25 33 41 6 10 14 32 20 8
29 33 37 6 14 22 28 24 20
29 37 45 6 18 30 28 20 12
33 37 41 6 22 38 28 16 4
37 41 45 6 26 46 24 20 16
47 43 39 10 14 18 24 16 8
47 39 31 10 18 26 20 16 12
47 35 23 10 22 34 20 12 4
47 31 15 10 26 42 16 12 8
47 27 7 14 18 22 12 8 4
43 39 35 14 22 30
43 35 27 14 26 38
43 31 19 14 30 46
43 27 11 18 22 26
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Posted by Charlie
on 2006-07-04 13:43:37 |
re: solution
